Your expectations are rather aggressive for a DC motor.
First - 40Nm (350in-lbs) is A LOT of torque! Ex: A max rated torque for 1/4-20 bolt is only 75 in-lb (8.5Nm).
Second - The mechanical power of a motor results from RPMTorque. 40Nm100rpm is 0.56hp (420W at 100% efficiency). That is A LOT, about 1/2 of what today's high end cordless drills can do. Fortunately it looks like you aren't expecting high torque at the high RPM so actual power will be lower; but, those numbers are likely to affect your motor size (unless you are going to use a transmission). You will probably need to start thinking about a torque curve.
Regarding DC motors: They rely on higher RPM to deliver higher power rather than higher Torque. This has to do with the physics of the motor. High Torque with a DC motor is going to require some sort of a "mechanical advantage".
Here are some design options to consider.
- (Metal) Gears/Gearbox. Planetary gearbox could do. Plastic gears (at least for the load end) are likely going to fail at high torque. They simply can't handle the sheer. You can get some that are pretty small. Here is gear motor from Motion Dynamics that can to 40Nm. Here is one from Midwest Motion that can also do 40Nm (Note: Both use Planetary gearboxes and are pretty slow and no where close to the power you are looking for).
- A slight variation of the gearbox (but work mentioning separately) is a worm gear/drive. This can get you a lot of mechanical advantage; but, it will turn the axis or rotation by 90deg.
- Use a cord-and-spindle and pulleys if needed to gain additional mechanical advantage (this does great for pulling; but, you are going to need a spring for return). Think garage door opener (sort of). Also think human arm (muscles only pull). Other linear-motion leverage options are leadscrews and rack-and-pinion gears.
- Hydraulics (as mentioned). This is how car brakes, clutches, and power steering do it. It allows you to move the motor off the arm. This is pretty common for large walking robots like Boston Dynamics Atlas.
Note: AC motors are more efficient than DC motors if you don't need positional control. That is likely why Tesla uses them in their cars.